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Load packages and data

library(tidyverse)
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library(plotly)
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##     layout
library(ggcorrplot)
library(htmltools)
data <-
  readRDS("data/gemeinderatswahlen_alldata.rds")
options(scipen = 20)
theme_set(theme_minimal())

Unvariate Statistics

data  %>%
  select(where(is.numeric)) %>%
  reshape2::melt(.) %>%
  ggplot(., aes(x = value)) + 
    facet_wrap(~variable, scales = "free") + 
    geom_histogram()
## No id variables; using all as measure variables
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## dropped
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## Warning: Removed 7925266 rows containing non-finite values (stat_bin).

ggsave("plots/histograms.svg", width = 45, height = 45, units = "cm")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 7925266 rows containing non-finite values (stat_bin).

Bivariate descriptive statistics

Correlations

data %>%
  select(where(is.numeric)) %>%
  cor(., use = "pairwise.complete.obs") %>%
  ggcorrplot::ggcorrplot(
    .,
    colors = c("red", "white", "blue"),
    #lab = TRUE,
    digits = 1
    )
## Warning in cor(., use = "pairwise.complete.obs"): Standardabweichung ist Null

ggsave("plots/bivariate_correlations.svg", width = 45, height = 45, units = "cm")

Cutoffs

Define cutoffs for each state, in some cases depending on years (if reforms took place) and whether town is muinicipality (“Gemeinde”) or “district-free city” (“kreisfreie Stadt”).

“th” stands for threshold.

th_1_muni_since_2012 <- c(70, 200, 750, 1250, 2500, 5000, 10000, 15000, 25000, 35000, 45000)
th_1_muni_before_2012 <- c(70, 200, 750, 1250, 2000, 5000, 10000, 15000, 25000, 35000, 45000)
th_1_krefr <- c(150000)
#th_3 <- c(500, 1000, 2000, 3000, 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 15000, 20000, 25000, 30000, 40000, 50000, 75000, 100000, 125000, 150000, 175000, 200000, 250000, 300000, 350000, 400000, 500000, 600000)
th_5 <- c(5000, 8000, 15000, 30000, 50000, 100000, 250000, 400000, 550000, 700000)
th_6 <- c(3000, 5000, 10000, 25000, 50000, 100000, 250000, 500000, 1000000)
th_7 <- c(300, 500, 1000, 2500, 5000, 7500, 10000, 15000, 20000, 30000, 40000, 60000, 80000, 100000, 150000)
th_8 <- c(1000, 2000, 3000, 5000, 10000, 20000, 30000, 50000, 150000, 400000)
th_9 <- c(1000, 2000, 3000, 5000, 10000, 20000, 30000, 50000, 100000, 200000, 500000) # Except Nuremburg and Munich
th_10 <- c(10000, 20000, 30000, 40000, 60000, 100000)
th_12_muni_since_2008 <- c(700, 1500, 2500, 5000, 10000, 15000, 25000, 35000, 45000)
#th_12_muni_before_2008 <- c(200, 700, 1500, 2500, 5000, 10000, 15000, 25000, 35000, 45000)
th_12_krefr <- c(100000, 150000)
th_13 <- c(500, 1000, 1500, 3000, 4500, 6000, 7500, 10000, 20000, 30000, 50000, 75000, 100000, 150000)
th_14 <- c(500, 1000, 2000, 3000, 5000, 10000, 20000, 30000, 40000, 50000, 60000, 80000, 150000, 400000)
th_15_since_2014 <- c(1000, 2000, 3000, 5000, 10000, 20000, 30000, 50000, 150000, 300000)
th_15_before_2014 <- c(100, 500, 1000, 2000, 3000, 5000, 10000, 20000, 30000, 50000, 150000, 300000)
th_16 <- c(500, 1000, 2000, 3000, 5000, 10000, 20000, 30000, 50000, 100000, 200000)

Cutoff rule changes

01 Schleswig-Holstein (with “2002” representing the 1998 election): You can clearly see municipalities with 2000-2500 inhabitants “overlapping” in terms of total seats (compare 2018 to prior elections):

data %>%
  filter(state == 1 & exact_pop > 1250 & exact_pop <= 5000 & (election_year == 1 | year == 2002)) %>%
  ggplot() +
  geom_point(aes(x = exact_pop, y = total_seats, colour = as.factor(year)))

12 Brandenburg – population data only for 2019:

data %>%
  filter(state == 12 & exact_pop <= 700 & election_year == 1) %>%
  ggplot() +
  geom_point(aes(x = exact_pop, y = total_seats, colour = as.factor(year)))

15 Saxony-Anhalt (with “2002” representing the 1999 election): After redistricting in 2007, municipalities are larger than before (and far less exist).

data %>%
  filter(state == 15 & exact_pop <= 1000 & (election_year == 1 | year == 2002)) %>%
  ggplot() +
  geom_point(aes(x = exact_pop, y = total_seats, colour = as.factor(year)))

data %>%
  filter(state == 15 & exact_pop <= 1000 & (election_year == 1 | year == 2002)) %>%
  group_by(year) %>%
  summarize(mean = mean(exact_pop), median = median(exact_pop), n = n())

Inhabitants vs. council size for each state separately

States with no changes in cutoffs and no distinction between municipalities and “district-free cities” only (i. e. 01, 12, 15 excluded). 03 Lower Saxony excluded due to missing data. Vertical bars indicate cutoffs.

plot_list <- htmltools::tagList()
for (s in c(5:10, 13, 14, 16)) {
  df_subset <- data %>%
    filter(state == s & (election_year == 1 | year == 2002))
  correlation <-
    cor(df_subset$exact_pop, df_subset$total_seats, use = "pairwise.complete.obs") %>%
    round(., 2)
  plot <- df_subset %>%
    ggplot() +
    geom_vline(xintercept = get(paste0("th_", s))) +
    geom_point(aes(
      x = exact_pop,
      y = total_seats,
      colour = as.factor(year),
      text = paste("town:", town)
    )) +
    labs(title = paste0("State: ", s, "; linear correlation: ", correlation)) +
    scale_x_log10()
  plot_list[[s]] <- plotly::ggplotly(plot)
}
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plot_list

We observe some countries where cutoffs play a huge role (06 Hesse, 07 Rhineland-Palantine, 09 Bavaria, 10 Saarland, 16 Thuringia). In other states they do not and total_seats spreads more (05 North Rhine-Westphalia, 08 Baden-Württemberg, 14 Sachsen-Anhalt).

“Special” states:

Red vertical lines indicate a cutoff that did not exist over the entire time period.

# 01 Schleswig-Holstein
df_subset <- data %>%
  filter(state == 1 & (election_year == 1 | year == 2002) & kreisfreie_stadt == 0)
correlation <-
  cor(df_subset$exact_pop, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  geom_vline(xintercept = th_1_muni_since_2012) +
  geom_vline(xintercept = c(2000, 2500), colour = "red") +
  geom_point(aes(
    x = exact_pop,
    y = total_seats,
    colour = as.factor(year),
    text = paste("town:", town)
  )) +
  labs(title = paste0("State: ", 1, "; linear correlation: ", correlation, "; no kreisfreie Städte")) +
  scale_x_log10()
## Warning: Ignoring unknown aesthetics: text
plotly::ggplotly(plot)
# 12 Brandenburg
df_subset <- data %>%
  filter(state == 12 & (election_year == 1 | year == 2002) & kreisfreie_stadt == 0)
correlation <-
  cor(df_subset$exact_pop, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  geom_vline(xintercept = th_12_muni_since_2008) +
  geom_point(aes(
    x = exact_pop,
    y = total_seats,
    colour = as.factor(year),
    text = paste("town:", town)
  )) +
  labs(title = paste0("State: ", 12, "; linear correlation: ", correlation, "; no kreisfreie Städte")) +
  scale_x_log10()
## Warning: Ignoring unknown aesthetics: text
plotly::ggplotly(plot)
# 15 Saxony-Anhalt
df_subset <- data %>%
  filter(state == 15 & (election_year == 1 | year == 2002))
correlation <-
  cor(df_subset$exact_pop, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  geom_vline(xintercept = th_15_before_2014, colour = "red") +
  geom_vline(xintercept = th_15_since_2014) +
  geom_point(aes(
    x = exact_pop,
    y = total_seats,
    colour = as.factor(year),
    text = paste("town:", town)
  )) +
  labs(title = paste0("State: ", 15, "; linear correlation: ", correlation)) +
  scale_x_log10()
## Warning: Ignoring unknown aesthetics: text
plotly::ggplotly(plot)

12 Brandenburg also has quite a strong relationship but no population data beyond 2019. 15 Saxony-Anhalt may have had some special rules after 2007 county reform (to do: investigate)!

“Expected” number of seats vs. actual seats number

Expected is what I deemed the size of the local parliament based on laws and ignoring voluntary reductions as well as “overhang seats”

df_subset <- data %>%
  filter((election_year == 1 | year == 2002))
correlation <-
  cor(df_subset$by_law_seats, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  #geom_vline(xintercept = th_1_muni_since_2012) +
  #geom_vline(xintercept = c(2000, 2500), colour = "red") +
  geom_point(aes(
    x = by_law_seats,
    y = total_seats,
    colour = as.factor(state),
    text = paste("town:", town, "<br>year:", year)
  )) +
  labs(title = paste0("All states", "; linear correlation: ", correlation))
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plotly::ggplotly(plot)

Inhabitants vs. council size for all states

Linear difference:

df_subset <- data %>%
  filter(election_year == 1 | year == 2002)
correlation <-
  cor(df_subset$exact_pop, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  geom_vline(xintercept = 0) +
  geom_point(aes(
    x = diff_to_cutoff,
    y = total_seats,
    colour = as.factor(state),
    #shape = as.factor(state),
    text = paste("town:", town, "<br>year:", year)
  )) +
  labs(title = paste0("All states; linear correlation: ", correlation))
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plotly::ggplotly(plot)

Using the Egger and Koethenbuerger (2010) calculation steps: \[\tilde{N_i} = N_i/N_d\] with \(N_i\) as the relevant actual population size and \(N_d\) as the respective thresholds.

df_subset <- data %>%
  filter(election_year == 1 | year == 2002)
correlation <-
  cor(df_subset$inhabs_rel_to_cutoff, df_subset$total_seats, use = "pairwise.complete.obs") %>%
  round(., 2)
plot <- df_subset %>%
  ggplot() +
  geom_vline(xintercept = 0) +
  geom_point(aes(
    x = inhabs_rel_to_cutoff,
    y = total_seats,
    colour = as.factor(state),
    #shape = as.factor(state),
    text = paste("town:", town, "<br>year:", year)
  )) +
  labs(title = paste0("All states; linear correlation: ", correlation))
## Warning: Ignoring unknown aesthetics: text
plotly::ggplotly(plot)

Inhabitants and public spending for each state separately

Relationship between inhabitants and public spending for those states that did not change cutoffs:

plot_list <- htmltools::tagList()
for (s in c(5:10, 13, 14, 16)) {
  df_subset <- data %>%
    filter(state == s & (election_year == 1 | year == 2002))
  correlation <-
    cor(df_subset$exact_pop, df_subset$ln_gross_expenditure_pc, use = "pairwise.complete.obs") %>%
    round(., 2)
  plot <- df_subset %>%
    ggplot() +
    geom_vline(xintercept = get(paste0("th_", s))) +
    geom_point(aes(
      x = exact_pop,
      y = ln_gross_expenditure_pc,
      colour = as.factor(year),
      text = paste("town:", town)
    )) +
    labs(title = paste0("State: ", s, "; linear correlation: ", correlation)) +
    scale_x_log10() +
    scale_y_log10()
  plot_list[[s]] <- plotly::ggplotly(plot)
}
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plot_list
rm(s, plot_list, plot, df_subset)

Relationship between inhabitants and public spending per capita for those states that did not change cutoffs:

plot_list <- htmltools::tagList()
for (s in c(5:10, 13, 14, 16)) {
  df_subset <- data %>%
    filter(state == s & (election_year == 1 | year == 2002))
  correlation <-
    cor(df_subset$exact_pop, df_subset$ln_gross_expenditure_pc, use = "pairwise.complete.obs") %>%
    round(., 2)
  plot <- df_subset %>%
    ggplot() +
    geom_vline(xintercept = get(paste0("th_", s))) +
    geom_point(aes(
      x = exact_pop,
      y = ln_gross_expenditure_pc,
      colour = as.factor(year),
      text = paste("town:", town)
    )) +
    labs(title = paste0("State: ", s, "; linear correlation: ", correlation)) +
    scale_x_log10()
  plot_list[[s]] <- plotly::ggplotly(plot)
}
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plot_list
rm(s, plot_list, plot, df_subset)